Transcript 4 RC Circuits and Household Safety

-RC Circuits
-Household
Safety
AP Physics C
Mrs. Coyle
RC Circuits
• Resistors and Capacitors in the circuit.
Two Situations for RC
Circuits
Steady State
• Occurs when the
capacitor is fully charged
• There is no current in the
branch of the fully
charged capacitor (it acts
as an open circuit)
• The current in the other
braches is constant
(steady state)
Variable Current
• While the capacitor is
charging or discharging
Charging a Capacitor in an RC Circuit
• When the switch is closed, the
capacitor starts to charge and
the current is at maximum.
• The current decreases as the
capacitor continues to charge
until it reaches its maximum
charge (Q = CVc)
• The potential difference
increases until a maximum Vc.
• Once the capacitor is fully
charged, the current is zero.
Vc
Steady State RC Circuit
• When the capacitor is fully charged no current
flows through the branch it is in.
• The capacitor has its maximum voltage.
• Sign convention for the capacitor voltage is
the same as a battery:
Vc is (+) when we traverse
from the (–) to the (+) plate of the capacitor
(low potential to high potential)
-| |+
Example 1: What is the voltage and charge
of the capacitor at steady state?
E=10V
Vc
C=2μF
• Ans: 10V, 20μC
Charging a Capacitor in an RC Circuit
• The charge on the
capacitor increases
exponentially with time
q =Q(1 – e-t/RC)
t is the time constant
t = RC
(unit: sec)
• To find current as a
function of time
differentiate:
q =C E (1 – e-t/RC)
ε t RC
I( t )  e
R
Example 2
• Derive q =Q(1 – e-t/RC).
• Hint: use Kirchhoff’ loop rule and substitute
I=dq/dt
Time Constant and U
• In a time t=RC then q=Q(1-e-1)=0.632Q
• The time constant represents the time
required for the charge to increase from
zero to 63.2% of Q maximum.
• The energy stored in the charged
capacitor is U=½ Qe = ½ Ce2
Discharging a Capacitor in an RC Circuit
q = Qe-t/RC
• The charge
decreases
exponentially
Discharging a Capacitor in an RC Circuit
• At t = t = RC, q= Q e-1 = 0.368 Qmax
• In one time constant, the capacitor loses 63.2%
of its initial charge
• Current:
dq
Q t RC
I t  

e
dt
RC
Example 3
• When the switch is
closed at steady state
(when the capacitor is
fully charged), what is
the charge of the
capacitor?
• Hint: Apply Kirchhoff’s
Rules
• Ans: 8.0 x 10-6 C
Household Wiring
• The utility company distributes
electric power to individual
homes by a pair of wires (one
live and one neutral-ground)
with a V of 120V
• The potential of the neutral
wire is taken to be zero
• Each house is connected in
parallel with these wires
• The current and voltage are
alternating
Short Circuit
• A short circuit occurs when almost zero
resistance exists between two points at different
potentials
• This results in a very large current
• In a household circuit, a circuit breaker will open
the circuit in the case of an accidental short
circuit
– This prevents any damage
Effects of Various Currents
• 5 mA or less
– can cause a sensation of shock
– generally little or no damage
• 10 mA
– muscles contract
– may be unable to let go of a live wire
• 100 mA
– if passing through the body for 1 second or less, can
be fatal
– paralyzes the respiratory muscles
Household Safety
• Why should you not plug too many
appliances in the same outlet?
• What is the role of a circuit breaker?
• Why should you not touch an electric
appliance with wet hands?
• What causes human injury current or
voltage?
• Why is grounding used?
More Effects
• In some cases, currents of 1 A can
produce serious burns
– Sometimes these can be fatal burns
• No contact with live wires is considered
safe whenever the voltage is greater than
24 V
Ground Wire
Ground-Fault Interrupters (GFI)
• Special power outlets
• Used in hazardous areas
• Designed to protect people from electrical
shock
• Senses currents (of about 5 mA or
greater) leaking to ground
• Shuts off the current when above this level